Effect of path length on valve tray columns: Experimental study

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To link to this article : DOI:10.1016/j.ces.2014.12.010

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To cite this version : Brahem, Rim and Royon-Lebeaud, Aude and

Legendre, Dominique

Effect of path length on valve tray columns:

Experimental study. (2015) Chemical Engineering Science, vol. 126.

pp. 517-528. ISSN 0009-2509

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Effect of path length on valve tray columns: Experimental study

Rim Brahem

a,n

, Aude Royon-Lebeaud

a

, Dominique Legendre

b

a_{IFP Energies nouvelles, Rond-point de l'échangeur de Solaize, BP 3, 69360 Solaize, France} b

Institut de Mécanique des Fluides de Toulouse (IMFT), 2 Allée du Professeur Camille Soula, 31400 Toulouse, France

Keywords:

Valve trays hydrodynamics Interfacial area

Absorption columns Scale up

Path length

a b s t r a c t

Experimental measurements of hydrodynamic and interfacial area parameters are carried out over two rectangular pilot scale valve tray columns. The effect of tray path length on extrapolation between the two columns is studied and phenomenological correlations for hydrodynamic and interfacial area are proposed. Correlations are compared both to literature and to industrial results showing good agreement and a significant improvement for the prediction of industrial conditions. Discrepancies preventing an accurate description of industrial trends are highlighted through comparison between typical emulsion height profiles on both columns.

1. Introduction

Natural gas commercialisation is subject to constraining envir-onmental and operational specifications. Such specifications require treatment of gas streams in order to remove components such as water, heavy hydrocarbons, acid gases (CO2, H2S, organic sulphur

compounds, COS, CS2, HCN), nitrogen oxides (NOx), sulphur dioxide

(SO2), nitrogen compounds, volatile organic compounds (VOCs),

volatile chlorine compounds (HCl, Cl2, …) or volatile fluorine

compounds (HF, SiF4,…) (Kohl and Nielsen, 1997). Depending on

their initial composition and required product specifications, gas streams are processed through several units (dehydration, desul-phurisation, acid gas removal,_{…). For the acid gas removal unit,} different kinds of technologies are employed: physical or chemical absorption, permeation, redox or cryogenics. The technology choice is mainly based on the concentration of acid compounds, selectivity to a specific compound and specifications of final products.

The most common technology is gas–liquid absorption using amines solutions.

Valve trays are widely used as contactors for absorption columns because of their relatively low cost and their better performance for specific situations. Within the gas sweetening process context, absorption columns design depends greatly on the accurate deter-mination of hydrodynamics and mass transfer parameters related to gas–liquid contactors as these have important effects on column effectiveness and operability. Actually this design relies on empirical correlations established on pilot scale units. However considerable discrepancies exit between sets of correlations encountered in the literature which makes optimisation of column design difficult to achieve. Experimental works have been carried out on hydrody-namics and mass transfer mainly on sieve trays, and little on valve trays (sieve trays:Zuiderweg and Harmens, 1958; Mc Allister et al., 1958; Barker and Self, 1962; Kister and Haas, 1988; Colwell, 1981; Zuiderweg, 1982; Bennett et al., 1983; Fasesan, 1987; valve trays:

Scheffe, 1984; Pohorecki and Moniuk, 1988; Peytavy et al., 1990; Liang et al., 2008). Yet malfunctions on industrial columns still occur (Kister, 2003; Kister and Olsson, 2011), even for sieve trays which have been most studied. Divergences between literature correlations

could be attributed to the great number of influent parameters (geometric, operational and physicochemical), the impacts of which have not all been studied thoroughly.

For a given system and an established operating condition, the overall hydrodynamic parameters on trays that are related to absorption effectiveness are mainly clear liquid height hLc,

emul-sion height hFeand mean liquid fraction

α

L. These parameters are

related to each other through the following expression:

hL¼

α

LhFe ð1Þ

Correlations reported in the literature for these three para-meters can be sorted into two groups based on the phenomen-ological description adopted for the gas–liquid emulsion flow.

The most commonly used description is the one established on the hypothesis of a homogeneous mixture. This postulate justifies the use of Francis's equation describing the height over an exit weir of a stationary fluid flow. When considering the gas–liquid emulsion rate in the Francis equation, correlations for the clear liquid height over the tray are proposed in experi-mental studies with the following form (Stichlmair, 1978; Hofhuis, 1980; Colwell, 1981; Bennett et al., 1983; El Azrak, 1988; Liang et al., 2008): hLc¼

α

LhFe¼

α

Lhwþ C

α

LL2 g !1=3 ð2Þ L is the liquid loading defined as

L¼QL

Lw ð3Þ

where QL is the liquid rate, Lw and hW are the width and the

height of exit weir respectively, g is the gravitational accelera-tion and C is a constant taking into account the fricaccelera-tion on the tray.

The second phenomenological description used for the gas– liquidflow is the trajectory model. In this model the liquid motion towards the tray exit is the effect of droplet ejection over the exit weir. This description points out the importance of momentum transfer from the ascending gas to the cross liquid flow. As a consequence, the_{flow parameter FP, representing the ratio of the} liquid to the gas inertia, is used for correlations describing hydrodynamic parameters: FP¼ ffiffiffiffiffiffi

ρ

L

ρ

G r _U L UG ð4Þ

where ULis the horizontal liquid velocity defined as

UL¼

QL

hLc Lw ð5Þ

UGis the vertical gas velocity toward the active area Aadefined as

UG¼

QG

Aa ð6Þ

and

ρ

L and

ρ

Gare the liquid and gas densities, respectively. To

access the horizontal liquid velocity UL, the knowledge of clear

liquid height hLc is required. Thus for empirical correlations,

different authors have used theflow ratio

Ψ

instead of theflow parameter FP (Dhulesia, 1983, 1984; Békássy-Molnár and Mustafa,

1991; Mustafa and Békássy-Molnár, 1997):

ψ

¼ FP  hLc¼ ffiffiffiffiffiffi

ρ

L

ρ

G r _L UG ð7Þ

The clear liquid height is then written as a power law of

ψ

:

hLc¼ A

ψ

α ð8Þ

Several studies agree well with the fact mean liquid fraction

α

Lis

mainly dependent on gas inertia (Bennett et al., 1983; Liang et al., 2008). Some efforts have been made to propose dimensionally coherent correlations by using the Froude number Fr, comparing gas inertia to liquid weight on the tray (Hofhuis, 1980; Colwell, 1981; Zuiderweg, 1982; Chen and Fan, 1995):

Fr¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ρ

GU 2 G g

ρ

_LhLc s ð9Þ The interfacial area and the mass transfer coefficients on both liquid and gas sides are also important parameters for column design. For these parameters less phenomenological descriptions can be found and the reported expressions are mainly put under a power law form (Badssi et al., 1988; Peytavy et al., 1990; Pohorecki and Moniuk, 1988). Furthermore little experimental work on the mass transfer parameters has been made on reasonably large pilot units to account for the hydrodynamic effects (Scheffe, 1984; El Azrak, 1988; Liang et al., 2008). For these parameters the choice of a characteristic liquid velocity seems more problematic as well. Indeed, depending on the studies, two characteristic liquid velo-cities are encountered: the liquid loading L or the liquid velocity ULabased on active area Aa:

ULa¼

QL

Aa ð10Þ

The effect of column dimensions which impact scalability to larger sizes has been less studied. Studying hydrodynamics on sieve trays,Hofhuis (1980)used two different size columns and pro-posed dimensional coherent correlations for hydrodynamic para-meters and regime transitions. Other works have used different sets of experimental data and have indirectly considered the effect of the column size (Colwell, 1981; Zuiderweg, 1982; Bennett et al., 1983; Chen and Fan, 1995).

Krishna and Van Baten (2003) have carried out a CFD study where the effect of column diameter has been investigated through the modelling of two different columns. In this work the authors showed an important impact of scale effects especially on the mixing characteristics.

In the present work the effect of path length LP, the distance

travelled by the liquid on a tray between the entrance and the exit weir, is investigated by carrying out hydrodynamic and interfacial area measurements. Two different path lengths are considered: LP¼0.36 m and LP¼0.96 m. This geometric parameter has not been

studied thoroughly in literature.Table 1gives some examples of characteristic path lengths LPfrom the literature and shows that

some works have been conducted on relatively small path lengths LPin comparison to industrial units.

The two columns considered in this work are presented in

Section 2. Section 3is dedicated to the comparison of hydrody-namic parameters and interfacial area measurements. InSection 4, some attempts are made in order to propose phenomenological

Table 1

Examples of LP(m) values in literature versus industrial units.

Piqueur and Verhoeye (1976)

Bennett et al. (1983)

Mustafa and Békássy-Molnár (1997) Fasesan (1987) Uys et al. (2012) Liang et al. (2008) Dhulesia (1984) Industrial units 0.15 0.15 0.28 0.43 0.475 0.53 0.89 0.5/0.8

and dimensionally coherent correlations for clear liquid height hLc,

mean emulsion height hFe, mean liquid fraction

α

Land interfacial

area per net area a0. The proposed correlations are compared to correlations from the literature inSection 5.Section 6discusses the application of the proposed correlation to industrial cases and presents future work.

2. Experimental set up

The present experimental study has been realized on two rectan-gular pilot columns, C2 and C3, having the same geometrical char-acteristics but a different path lengths LP(seeFig. 1a). The total tray

pressure drop (

Δ

PTray) and the emulsion pressure drop (

Δ

PEmulsion)

were measured using Rosemount manometers (seeFig. 1).

Δ

PEmulsion

was measured at four different positions and a mean value was con-sidered. Assuming that

Δ

PEmulsionis mainly generated by the liquid

weight over the tray, the clear liquid height hLcwas evaluated as

hLc¼

Δ

PEmulsion

ρ

Lg ð11Þ

The emulsion height measurements were made by post-processing video recordings. For each video a mean emulsion profile is generated, from which a mean emulsion height hFeover the tray is

measured. More details on hydrodynamic measurements and image processing can be found inBrahem et al., 2013a.

The interfacial area was measured using an indirect reactive absorption method. The reaction of CO2absorbed in an aqueous

sodium hydroxide solution is employed (400 ppm CO2in air/0.1 N

NaOH in water). This method has been validated for interfacial

area measurements of structured packing byAlix et al. (2011). The absorption chemistry can be described by the following set of reactions:

CO2ðgÞ2CO2ðlÞ 1st

CO_2ðlÞþOH_2HCO 3 2nd

HCO3þOH2CO23 þH2O 3rd ð12Þ

The 1st reaction represents the physical absorption of CO2at the

interface. Equilibrium is assumed and represented by the Henry's law: CL_CO;i 2¼ PG_CO;i 2 He ð13Þ

The rate of the 3rd reaction is assumed to be much higher than that of the 2nd reaction (Pinsent et al., 1956; Pohorecki and Moniuk, 1988). Thus the overall kinetic rate is controlled by the 2nd reaction (Pohorecki and Moniuk, 1988):

r¼ k2COHCCO2 ð14Þ

In the present study the hydroxide concentration is largely higher than the CO2concentration, so that the reaction can be considered

as pseudo 1st order: r_{¼ k}2C0OHCCO2¼ k

0_C

CO2 ð15Þ

The doublefilm absorption model is considered with which mass transfer from gas to liquid is considered to take place through two thin layers located one on each side of the interface. Assuming equilibrium at the interface and neglecting the resistance to the mass transfer on the gas side (PGCO;i2 P

G;b

CO2), the CO2absorbedflux

Tray characteristics Column C2 Column C3 Total length (m) 0,66 1,26 Path length LP(m) 0.36 0.96

Total cross section

area AT(m²) 0,13 0,24 Active area Aa (m²) 0,07 0,18 Perforated area Ah(m²) 0,011 0,032 Ratio of perforated area (% of Aa) 15.7 17.6 Weir height hw(m) 0,065 Weir length Lw(m) 0,1905 Plates/ column 4 Tray spacing (m) 0.455 Valves characteristics Type V4R GLITSCH Valves / tray 9 27 Minimum lift (m) 0.001 Maximum lift (m) 0.009 Valve diameter (m) 0.0475 Hole diameter (m) 0.039 valves / m² of active area 122

is controlled by the mass transfer absorption rate in the liquid:

ϕ

¼ aUE UkL CLCO;i2C L;b CO2   ¼ aUEUkL PG_CO;i 2 He C L;b CO2 ! ð16Þ where

ϕ

is the CO2 absorbed flux, a the interfacial area, E the

enhancement factor taking into account the contribution of the reaction, kLthe liquid side mass transfer coefficient, CLCO;i2the CO2

concentration in the liquid at the interface, CL;bCO2 the CO2

concen-tration in the liquid bulk and He the interfacial equilibrium constant (Henry's law). The enhancement factor depends on 3 parameters:

– The Hatta number Ha: Ha_¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi DLk2C0OH

q

kL ð17Þ

– The instantaneous enhancement factor, also known as a concentration-diffusion factor Ei¼ C0OH CiCO2 DOHL  DCO2 L ð18Þ – The ratio between the liquid volume per interfacial area and

the liquid_{film thickness} ZD¼

α

L a 1

δ

L¼

α

L a kL DCO2 L ð19Þ

In the case of a fast reaction for which Ha43 and ZDc1, the

enhancement factor can be approximated by the Hatta number E Ha and the CO2concentration in the liquid bulk is CL;bCO2 0.

Consequently the absorbedflux is written as

ϕ

¼ aU ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDLk2C0OH q _PG;b CO2 He ! ð20Þ Knowing the diffusion constant DL, the Henry's constant He and

the kinetic constant k2 (constants taken from Pohorecki and

Moniuk (1988)), the measurement of the CO2absorbedflux, the

CO2 pressure in the gas bulk and the hydroxide concentration

allow an indirect determination of the interfacial area a¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ϕ

DLk2C0OH q ðPG;b CO2=HeÞ ð21Þ A perfectly agitatedflow for the liquid phase and a plug flow for the gas phase are also assumed for the determination of the interfacial area. Two infrared analysers were used at the column entry and exit to measure the CO2concentrations. The hydroxide

concentration in the liquid was measured by titration with HCl.

3. Comparison between the two columns

The differences observed between correlations from the litera-ture are partially due to the use of different liquid and gas velocities in the experiments. For the liquid velocity two parameters are commonly used, either ULathe liquid velocity based on the active

area (Badssi et al., 1988; Scheffe, 1984) or L the liquid rate per weir length (or liquid loading) (El Azrak, 1988; Colwell, 1981). The liquid loading divided by the clear liquid height can be considered as a horizontal characteristic liquid velocity in opposition to ULawhich

represents a vertical characteristic velocity (seeFig. 2).

For the gas velocity, the kinetic factor (the square root of gas inertia) is usually employed. We consider here two different gas kinetic factors. Thefirst one uses the gas velocity based on the active area Aa while the second one considers the gas velocity

based on the net area An¼AaþAd where Ad is the area of one

downcomer (seeFig. 2). The gas kinetic factor toward Aais

Fa¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ρ

GU 2 Ga q ð22Þ with UGa¼ QG Aa ð23Þ

The gas kinetic factor toward Anis

Fn_¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ρ

GU2Gn q ð24Þ with UGn¼ QG An ð25Þ

In order to identify a pertinent characteristic liquid velocity allowing the comparison between the two columns, the results for the pressure drop, the liquid fraction, the emulsion height and the interfacial area are examined byfixing either the liquid velocity based on the active area ULaor the liquid loading L. Corresponding

plots of the total pressure drop and the mean emulsion height as function of the gas kinetic factor Fa are presented inFig. 3. When comparing results of pressure drop onFig. 3a to those onFig. 3b and results of mean emulsion height onFig. 3c to those onFig. 3d, representation of the experimental measurements on both col-umns by using the liquid loading L seems to be better adapted for extrapolation from the little column to the larger one.

As concerns the effect of gas velocity, the tray pressure drop is presented inFig. 4and the mean liquid fraction is shown inFig. 5at different liquid loadings L as a function of either the kinetic factor based on the active area Fa or the kinetic factor based on the net area Fn. The comparison of Figs. 4a and 5a to Figs. 4b and 5b suggests that Fa is better suited for the comparison of the selected hydrodynamic parameters (pressure drop, emulsion height, mean liquid fraction) especially for intermediate and high velocities. However for the interfacial area, the choice of Fn appears to be more pertinent as shown inFig. 6. This can be explained by the fact that the liquid–gas emulsion is not totally disengaged in the down-comer so that mass transfer also takes place in the downdown-comer.

As may be noticed trough the different plots of the present results for the considered gas and liquid velocities, the choice of a character-istic velocity is made difficult by the low sensitivity of the measured parameters to these velocities. In some configurations both proposed velocities can be representative. For instance, for pressure drop at low gas and liquid rates any velocity could be considered for extrapolation (Figs. 3a, b and4). For other parameters such as for mean emulsion height (Fig. 3c and d), the two characteristic velocities fail to super-impose the results from the two columns for moderate to high liquid

Fig. 2. Representative diagram of considered liquid (ULa, L) and gas (Fa, Fn)

loads. Failure tofind similar evolutions suggests that the hydrody-namic behaviour of the two columns is not totally identical. In particular, a sharp increase of the interfacial area is noticed when increasing the gasflow rate in the two columns but a different critical value is found (seeBrahem et al. (2013a,2013b) andBrahem (2013)

for a detailed description of the hydrodynamic regimes). The limit associated with the increase of interfacial area is related toflooding

and lies outside the nominal operating conditions of industrial columns and thus it is of little interest.

Though the similitude between the two columns is not perfect, the observed similarities encourage to consider the scale up and to propose correlations for the emulsion parameters: mean liquid fraction

α

L, mean emulsion height hFe, mean clear liquid height hLc

and interfacial area per net area a0.

Fig. 3. Comparison of tray pressure drop (a and b) and mean emulsion height (c and d) at afixed ULa(a and c) or at afixed L (b and d).

4. Correlations

In order to propose dimensional homogeneous expressions the choice of adapted parameters is discussed in this section. Once the general form of the correlation is settled, the least squares method is used to determine the constant parameters using the experimental data.

4.1. Mean liquid fraction

The Froude number has been considered by some authors to describe the evolution of the liquid volumetric fraction (Colwell, 1981; Hofhuis, 1980; Chen and Fan, 1995). This choice is also adopted here and the corresponding correlation is expressed

Fig. 5. Mean liquid volumetric fraction for different liquid loadings as a function of (a) gas kinetic factor Fa and (b) gas kinetic factor Fn.

Fig. 6. Interfacial area (a) as a function of Fa and (b) as a function of Fn.

as follows:

α

L¼

1

1þa1Frβ1 ð26Þ

Such an expression has also been suggested in previous studies (Azbel, 1963; Kim, 1966; Kawagoe et al., 1976; Colwell, 1981). The present experimental points yield to a1¼11.3 and

β

1¼0.54.

The comparison with experiments is presented inFig. 7a. For the sake of clarity only results on the larger column C3 are reported in this_{figure. The parity diagram shown in}Fig. 7b corresponds to the whole set of points obtained for the two columns. The twofigures indicate that the proposed correlation correctly describes the results obtained for the two columns.

4.2. Clear liquid height

Several authors have reported that the clear liquid height depends on the hydrodynamic regime (Dhulesia, 1984; El Azrak, 1988; Mustafa and Békássy-Molnár, 1997; Békássy-Molnár and Mustafa, 1991). Correlations for the clear liquid height for each hydrodynamic regime are proposed by Hofhuis (1980) and

Mustafa and Békássy-Molnár (1997). Hofhuis suggests a transition between the emulsion and the spray regimes for a critical value of the flow parameter FP (square root of liquid to gas inertia) between FP¼3 and FP¼4. Békássy-Molnár and Mustafa (1991) proposed correlations that are dependent on the hydrodynamic regime through theflow ratio

Ψ

(¼FP*hLc).

Taking these studies into account, our results for the clear liquid height are presented in term of theflow ratio

Ψ

(seeFig. 8).

The transition limit is observed for aflow parameter of 4 which is coherent with previous studies (Hofhuis, 1980; Zuiderweg, 1982). For both main hydrodynamic regimes, a correlation for the clear liquid height is determined.

4.2.1. Emulsion regime

For the emulsion regime, the two phaseflow over the exit weir is commonly described as homogeneous. This description leads to an expression for the clear liquid height under the following form: hLc¼

α

Lhwþ a2

α

L

L2 g

!1=3

ð27Þ This form arises from the well-known Francis equation for mass conservation of a stationaryfluid flow over a weir. Regres-sion of our results in the emulRegres-sion regime gives a2¼1.315.

4.2.2. Spray regime

For the spray regime, the trajectory model is usually used to describe the liquidflow on the tray. No explicit mathematical form can be easily obtained from this description. In the literature (Mustafa and Békássy-Molnár, 1997; Dhulesia, 1984), theflow ratio

ψ

is commonly used as the main correlating parameter. In this work we propose a cor-relation based on the two main parameters controlling theflow over the tray, namely the_{flow parameter FP and the Froude number Fr:} hLc¼

ψ

FP¼

ψ

a3Frβ2 ð28Þ

From our experiments we deduced a3¼0.85 and

β

2¼1.18.

Fig. 9compares the above correlations in both hydrodynamic regimes to the experiments. Good agreement is encountered for the two columns.

4.3. Mean emulsion height

The evolution of mean emulsion height can now be easily deduced from the mean liquid fraction and the clear liquid height by using relation(1):

hFe¼

hLc

α

L

The corresponding results are reported inFig. 10where a satisfactory agreement with experimental results is shown. A deviation similar to the one noticed for both mean liquid fraction and clear liquid height is observed.

Fig. 9. Clear liquid height: (a) comparison between correlations and experiments for the column C3 for different liquid loadings and (b) parity diagram for the two columns. Fig. 8. Identification of the transition between the emulsion and the spray regimes.

4.4. Interfacial area

In order to propose a dimensionally homogeneous correlation for the interfacial area, we consider the volumetric interfacial area. This rate represents the specific interfacial area per unity of emulsion volume. The results obtained for the two columns show that the interfacial area divided by the net area An is more adapted for the description of the entire set of experimental points. To estimate a

total emulsion volume, the mean emulsion height is considered. Thus the rate of interfacial area is expressed as follows:

ai¼

a An hFe¼

a0

hFe ð29Þ

Several investigations on bubbling flows (Bouaifi et al., 2001; Majumder et al., 2006; Muroyama et al., 2013) express this rate of interfacial area as a function of the gas volumetric fraction and the

Fig. 10. Mean emulsion height: (a) comparison between correlations and experiments for the column C3 for different liquid loadings and (b) parity diagram for the two columns.

Fig. 11. Interfacial area: (a) comparison between experiments and correlation (33) for column C3 for different liquid loadings and (b) corresponding parity diagram.

maximum bubble size: ai¼ C

α

G

dB max ð30Þ

The maximum bubble size is determined by a critical Weber number WeCriticalthat compares the surface tension to the liquid inertia that

tends to break up the interface: WeCritical¼ C0

ρ

L

U2

σ

=dB max ð31Þ

For the present gas injection system, we can reasonably consider that the gas inertia controls the bubble size so that we can write dB max¼ C

σ

F2n

ð32Þ The consideration of gas fraction for the volumetric interfacial correlation under a power law form showed no relevant depen-dency for this reason liquid fraction was considered instead of gas fraction which leads to thefinal correlation form for interfacial area: a0¼_Ana ¼ hFe a4

F2 n

σ α

βL3 ð33Þ

From our experiments we obtain a4¼6454 and

β

3¼4.65.

The comparison between this correlation and the experiments is reported inFig. 11. For the larger column C3, the results are quite

satisfying, but for the smaller column C2, the correlation considerably underestimates the experimental results. This highlights the fact that the proposed correlation(33)does not re_{flect the phenomenological} mechanism responsible for the production of gas–liquid interface. In fact the form proposed is pertaining to the bubbling regimes whereas two phase_{flow on the tray is considerably different owing to the} existence of gas jets observed near the valves exits and the presence of an emulsion zone above them. It is possible that both gas jet dynamics and emulsion behaviour are different between the two columns.

5. Comparison to correlations from literature

Several empirical correlations have been proposed in previous works (Dhulesia, 1984; El Azrak, 1988; Mustafa and Békássy-Molnár, 1997; Liang et al., 2008; Scheffe, 1984; Peytavy et al., 1990). We have selected some of the most used correlations and compared them to the relations and experiments obtained in our study (Figs. 12a and 13a). We compared our correlations with experimental points issued from other studies (Figs. 12b and13b) for both clear liquid height and interfacial area.

Considering the clear liquid height, the correlations found in literature allow to estimate our experimental results with an error of 60%. Using our own correlation (27) & (28) reduces the difference over the full data base from the same literature down to 40% which is a notable improvement.

Considering the interfacial area, the literature correlations allow to estimate our experiments with an error of 60% while our correlation(33)permits to reduce the error over the full data base of the same literature to 50%. This dispersion is highly dependent on the method used to measure this parameter as it has large uncertainties that are related to the choice of the kinetic and the thermodynamic constants.

6. Application to industrial cases and effect offlow path length In order to evaluate the accuracy of the correlation for interfacial area, and in particular its extrapolability, some expressions from the literature (El Azrak, 1988; Scheffe, 1984; Liang et al., 2008) and from the present work are compared to experimental points acquired on industrial columns. The corresponding comparisons are presented in

Fig. 14.

Fig. 14 clearly shows that the proposed correlation allows to significantly decrease the dispersion related to industrial points compared to previous expressions. However none of the correlations

Fig. 13. Interfacial area: (a) comparison of correlations literature to present data and (b) present correlation (33)applied to literature data.

Fig. 14. Interfacial area from industrial columns compared to correlation (33) and correlations from literature.

including the relations proposed in this study succeed in properly describing the experimental points. The differences between pre-dicted values and experimental points exceed those due to experi-mental errors in the industrial measurements, indicating that some important phenomena are not considered in the proposed models.

A scale effect has been noticed when comparing results between the two columns. A perfect similitude is not be obtained even when considering different liquid and gas velocities.

Fig. 15reports the clear liquid height and the mean emulsion height for the two columns.

In Fig. 15a similar behaviour for hLc is noticeable with two

distinct zones when the gas velocity increases. The _{first zone} corresponds to the sharp increase of hLcand is characterised by an

important amount of weeping. The second zone corresponds to the subsequent drop in clear liquid height (Brahem et al., 2013a,2013b). The differences between the two columns lie in a lower dependency to the liquid load on the smaller column C2 and a higher dependency to the gas kinetic factor especially for the second zone. Fig. 15b reports the mean emulsion height. The results for the smaller column show a small dependency to both gas and liquid velocities. Values comparable to those of the large column C3 are only observable at low gas kinetic factors.

To better understand these discrepancies, typical emulsion profiles are compared between the two columns inFig. 17. The large column shows that for a _{fixed liquid loading and an increasing gas kinetic} factor four different behaviours can be identified (Brahem et al.,

2013a) while for the small column only three behaviours are observed (Brahem et al., 2013b). At low gas velocities a dumping regime with a highly oscillating profile but rather homogeneous along the tray is noticed for both columns. Upon increasing the gas velocity for C3 a channelling regime is followed by a homogeneous regime observed while for column C2 only a regime with a bell-shaped emulsion profile is noticed. Approaching flooding at high gas velocities a channelling phenomenon is noticed for C3 while emulsion profiles for C2 are transformed into a more parabolic form.

Thefirst channelling regime observed on the large column C3 has been referenced as the vapour cross flow channelling phe-nomena (Kister, 1993; Resetarits and Pappademos, 2001). This phenomenon is commonly attributed to the establishment of hydraulic gradient on the tray that has been noticed on both columns (seeFig. 16).

Kister (2006)stated that the crossflow channelling takes place for ratios of L/T superior to 2 with a perforated area ratio Ah/Aa

exceeding 15%, which is the case for C3 but not for C2. These geometric parameters could thus explain the settling of crossflow channelling on the larger column.

Aside from the cross channelling phenomena, the profiles for C2 are less dependent on the gas and the liquidflow rates. As shown inFig. 17b and c, the profiles for the two columns seem to be similar at both the entrance and the exit of the tray. This is due to the fact the profile is fully controlled by geometries imposed on the tray extremities. However, in the middle of the tray, the emulsion profiles differ. For the larger column, the path length LP

is large enough for the profile to become stable and independent of the extremities. However for the small column where LP is

rather short. This could explain the lower dependence of emulsion height on gas and liquid velocities as observed in column C2.

These observations highlight an intrinsic scale effect on the hydrodynamic behavior of the two phasesflow. Such behavioural change between small and large columns could help to explain the differences noticed between proposed correlations and industrial results.

In addition to geometric scaling effects, one of which is for example the existence of more or less large dead zone, the effects of physicochemical properties and their dependence on operating con-ditions (pressure and temperature) as well as on the gas and liquid compositions have not been investigated through this work. They are expected to influence hydrodynamic and mass transfer behaviours and could also be at the origin of the differences noticed between proposed correlations and industrial results.

Fig. 15. Comparison between the two columns at different liquid loads L as a function of gas kinetic factor Fa: (a) clear liquid height hLcand (b) mean emulsion height hFe.

Fig. 16. Mean deviation of the emulsion pressure drop at different horizontal positionsΔPFe,tap(e1–e4: seeFig. 1a) toward the mean emulsion pressure dropΔPFe, meanon the 4 positions. The taps are numbered according to their distance from the

7. Conclusions

Experiments have been carried out on two different path length columns to provide a wide data base for hydrodynamic parameters and interfacial area on valve trays. Correlations for liquid fraction, clear liquid and emulsion heights and interfacial area have been proposed based on phenomenological descriptions. These correlations reproduce the present experimental data with a maximum error of 40% for hydrodynamic parameters and 50% for interfacial area for the two columns considered. Moreover, compared to previous correla-tions (Liang et al., 2008; Scheffe, 1984; El Azrak, 1988), the one

proposed here for the interfacial area improves representativeness of available data from both literature and industrial tests.

However, the new relation proposed for the description of the interfacial area fails to take into account the scale effect in terms of path length because of a non-negligible impact of the boundary conditions for the small column. This dependence leads to differ-ent emulsion profiles and different regime transition point bet-ween the two columns. Moreover other parameters of influence, such as physicochemical ones, have not been considered. Their effects are expected to be important and thus have to be quanti_fied in the future.

Fig. 17. Emulsion profiles for the two columns (a) as a function of the distance from the liquid entry normalised by the path length Lp(b) as a function of the distance from

Nomenclature

Aa active or bubbling area (m²)

Ah perforated area (m2)

AT total column cross area (m2)

dh hole diameter (m)

dV valve diameter (m)

Fa kinetic gas factor based on velocity toward active area (Pa0.5₎

G gravity acceleration (m s2) hFe emulsion height on the tray (m)

hLc clear liquid height on the tray (m)

hw exit weir height (m)

L liquid loading or liquid_{flow rate per unit weir length} (m3_{m s}1₎

LD downcomer length (m)

LP lengthflow path (m)

LT total column length (m)

Lw exit weir length (m)

P pressure (Pa)

QG gasflow rate (m3s1)

QL liquidflow rate (m3s1)

Ts tray spacing (m)

UG,a gas velocity toward active area (m s1)

UG,h gas velocity toward perforated area (m s1)

UL liquid velocity defined in relation(5)(m s1)

UL,a liquid velocity toward active area (m s1)

CD friction coefficient (dimensionless)

FP0 flow parameter, represents the square root of the ratio between liquid inertia and gas inertia (dimensionless) Fr Froude number opposing gas inertia toward active area

to liquid weight on the tray (dimensionless)

Frh Froude number using gas velocity toward perforated area

(dimensionless) Greek letters

α

L mean liquid hold up on tray (dimensionless)

Δ

PDry valves (or tray) pressure drop measured in absence on

liquidflow (Pa)

Δ

PEmulsion pressure drop due to emulsion on tray (Pa)

Δ

PTray tray pressure drop (Pa)

Δ

PValves valves pressure drop measured in presence on liquid

flow (Pa)

μ

G/L gas/liquid viscosity (Pa s)

ρ

G gas density (kg m3)

ρ

L liquid density (kg m3)

Ψ

flow ratio opposing liquid loading time square root liquid density and kinetic gas factor (m)

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